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Ternary decision rules allowing for abstentions,besides Yea- and Nay-votes, are analyzed. The German Bundesrat serves as a prime example. We show that the decision-making efficiency of the Bundesrat would increase if abstentions were allowed. A general formula for the mean success margin of a ternary decision rule is derived assuming selfdual and permutationally invariant distributions. The ternary Penrose–Banzhaf model is discussed in detail, and the influence probabilities of voters and a rule´s influence sensitivity are evaluated.

Abstentions in the German Bundesrat and ternary decision rules in weighted voting systems